One of the methods used for the containment of formation fluids in a well is the use of a weighted drilling fluid, where the hydrostatic pressure of this fluid prevents fluid influx into the well. This method is considered passive, since no direct human intervention is needed for the effectiveness of this method, in contrast to, for example, a mechanical blowout preventer. As a well is drilled, a series of casings and liners are cemented to the formation. As illustrated in FIG. 1, which is a cross-sectional view of part of a well and the surrounding formation 110, the cementing process typically seals the weighted drilling fluid 106 within an annulus between the top of the cement 108 and the top of the casing 102 or the top of the liner 104. Typically, the weighted drilling fluid 106 in the annulus is inaccessible after cementing, particularly in subsea, deepwater wells. One property of the weighted drilling fluid 106 trapped within the annulus is that it increases in volume with an increase in temperature and that it decreases in volume with an increase in pressure. For example, the “ideal gas” has the following relation between volume V, pressure P and temperature T (R is a constant related to the type of gas):
  V  =            R      *      T        P  
It can be seen that an increase in temperature T causes an increase in volume V. It can also be seen that an increase in pressure P causes a decrease in volume V. Real wellbore fluids are more complex than this simple model, however. For example, various fluid models are described by Poling, et al. in The Properties of Gases and Liquids, Fifth Edition, McGraw-Hill Book Company, New York, N.Y., 2001, sections 4.43-4.46. Furthermore, the well casing has the properties of expanding due to temperature increase, internal pressure increase, and/or external pressure decrease. Details of this behavior are described, for example, by Timoshenko and Goodier in Theory of Elasticity, McGraw-Hill Book Company, New York, N.Y., 1970, pp. 68-71; by Halal and Mitchell in Casing Design for Trapped Annular Pressure Buildup, SPE Drilling & Completion, Society of Petroleum Engineers, Richardson, Tex., 1993, pp. 179-190; and by Halal, et al. in Multi-String Casing Design with Wellhead Movement, SPE Production Operations Symposium, Oklahoma City, Okla., 1997, pp. 477-484.
When the annulus is cemented, the drilling fluid contained in the annulus has a specific initial temperature and pressure profile. The initial pressure profile was chosen to have the proper passive properties to prevent fluid influx into the annulus and also to prevent fracturing of the formation adjacent to the annulus. As the well is drilled to deeper depths, well operations (e.g. circulation of drilling fluids, cementing operations, and/or shut-in periods), may alter the temperatures in the well. Altering the temperature will change the pressure in the closed annulus. For example, an increase in temperature would cause an increase in the fluid volume. This fluid volume increase in an enclosed volume will then result in a pressure increase, needed to preserve the original volume by compressing the fluid. The overall calculation is further complicated by the pressure and thermal behavior of fluids in other annuli and the pressure and thermal behavior of the casings and liners. The resulting pressure change in the annulus may adversely effect the passive pressure containment barrier by either falling below the formation pressure, allowing fluid influx, or by fracturing the formation, which will result in the loss of annulus fluid volume. In FIG. 2, for example, a graph based on modeled data for an actual well illustrates how the annulus pressure can decrease with time when circulating fluids have cooled the weighted drilling fluid in the annulus. This decrease in hydrostatic pressure has the potential to allow fluid influx, indicating a possible failure of the passive pressure containment barrier. Monitoring is therefore, recommended by API RP 96 or may be required by government regulations (e.g. BOEMRE) to ensure well control and containment of formation fluids.
Well Cat™, which is a commercial software application marketed by Landmark Graphics Corporation, and other applications have been used to predict and analyze temperature changes and pressure changes of the weighted drilling fluid used as a passive pressure containment barrier, however, such techniques are limited by their failure to use the results in an iterative workflow to monitor and evaluate the weighted drilling fluid as a passive pressure containment barrier.